This paper explores the ‘barrier’ effect that tensile and compressive twins exert upon propagation of dislocations and other twins in zirconium (Zr). We do so by pre-deforming textured Zr at liquid nitrogen to selectively induce either tensile or compressive twins; next we anneal the dislocations while preserving the twinning structure; finally we reload the material at room temperature, where only prism slip, pyramidal slip and tensile twins are active. An analysis of the yield stress upon reload, and of the subsequent hardening response allows us to conclude that the twins play a dominant role in determining the hardening, while dislocations only have a second order effect.